library(dplyr)
    library(tidyr)
    dummy_fun <- function(x, alpha){
    return(sum((x %>% unnest)^alpha))}


dummy_data <- data.frame(id =  c(rep(c(1:8), times = c(10,12,8,13,7,8,10,12))), x = rnorm(80)) %>%
  group_by(id) %>%
  nest() %>%
  ungroup()%>%
  rowwise %>%
  mutate(y = dummy_fun(data, 2)) %>%
  ungroup()%>%
  rename(obs = data)

nls.test <- nls(y ~ dummy_fun(x = obs , alpha), data = dummy_data, start = list(alpha = 1.5))